Feedback Control System, with the Controller Designed using Direct Synthesis Method - Coursework Example

 Process Control Coursework Table of Contents 1.0 Introduction 1 2.0. Feedback Control System, with the Controller Designed using Direct Synthesis Method 2 3.0. Feedback Control System with Closed-loop Ziegler-Nichols Empirical Method. 3 4.0. Smith Predictor control system designed using the Direct Synthesis Method 6 5.0. Simulation of the three control systems 8 6.0. Discussion and conclusion 10 1.0 Introduction The mostly used and simplest method employed in process control is referred to as feedback control loop. It involves comparison of the set point (SP) and the controlled process variable measurement to generate an error which is then used in deriving the final control element (FCE) correction action (Seborg, Edgar and Mellichamp 2011). The manipulated variable is usually changed by the controller output. The controller action could either be sluggish or aggressive, and it is based on the tuning as well as the internal control law applied (Seborg, Edgar and Mellichamp 2011). In an industrial chemical process, the concentration control loop could be represented by a 2nd order dynamics with a transmission delay. There are two second order time constant dynamics considered and they include T1 =4 min and T2=6 min respectively. The dead time and steady state gain are 12 min and 5 min respectively. The loop needs to be controlled in order to attain a first order desired dynamics with 2 minutes as the time constant(Td) as well as the s zero steady-state offset. In this regard, this exercise involves designing a feedback control system with the use of direct synthesis method using first order Taylor expansion. In this case, the controller was implemented with a standard industrial controller. Also closed loop Ziegler –Nichols empirical method was used. 2.0. Feedback Control System, with the Controller Designed using Direct Synthesis Method i). Identify the plant transfer function and the desired closed-loop system transfer function. Then, Design a feedback control system, with the controller designed using Direct Synthesis Method, where the time delay is approximated using the first-order Taylor expansion. Implement the controller with a standard industrial PID controller. Direct synthesis method is applied in designing a controller TF (Gc(s). In this case, the system’s closed loop transfer function (Glc) is equal to the desired closed–loop transfer function (Gr(s) The plant transfer function (transfer function from set-point to output) can be represented as below; For closed-loop system transfer function, Gr(s) is used to replace Gcl(s) in the above equation and the final equation becomes: At this stage, the desired transfer function is required to satisfy the performance requirements. In this case, first order transfer function is applied and the time constant to be considered should satisfy the requirement for the setting time: ) In order to design the feedback controller for the process with second order dynamic time constants of 4 min and 6 min, direct synthesis method was used as below: Basing on the above equation, the controller can be implemented with a standard industrial controller as below: The standard PID controller is; .In this regard, it can be affirmed that the controller is a PID controller with 3.0. Feedback Control System with Closed-loop Ziegler-Nichols Empirical Method. ii) Design a feedback control system with a PID controller designed using the closed-loop Ziegler-Nichols empirical method. The Simulink model used in the experiment to obtain the sustained output curve should be displayed. The sustained output curve should also be displayed. The controller design must be presented. One of the earliest control strategies is considered to be proportional integral derivative control and it was first implemented in pneumatic devices, then later in solid state as well as in vacuum analog electronics. This was before it was implemented in the current digital microprocessors. Its control structure is very simple and it could be understood easily by the plant operators who could tune it with ease. It has a broad application range since it has been proved satisfactory by several control systems using it. It is also known that several plants that are controlled by PID controllers have similar dynamics and this has made it possible for the controller parameters to be set accordingly with little plant’s information compared to complete mathematical model. The most common PID techniques used are closed loop and step reaction curve. Controller tuning enables process optimization as well as error minimization between the process variables and the set point. There are different controller tuning methods that include process reaction curve and trial and error method. Cohen-Coon and Ziegler-Nichols are the most commonly used methods and they are applied in cases there are no system mathematical model. In this case, Ziegler-Nichols method is only applied to both open and closed loop systems, but Cohen-Coon is solely used in open loop systems. There is no comparison of the output and input for open loop system. As indicated in figure 1 below, it can be observed that the error e(t) in PID controller can be used in producing the integral, proportional as well as the derivative actions and the signals generated are summed and weighed to produce a control signal (u(t) that is used to the plant model Figure 1. Simulink model of closed –loop control system With the use of the below table Controllers Kc P 0.5Kcr 0 PI 0.45Kcr Pcr/1.2 0 PID 0.6Kcr 0.5Pcr 0.125Pcr We will have; Therefore the PID controller transfer function is; Figure 2. Simulink model Figure 3. Sustained output curve It is observed that despite the PID controller having a derivative in the feedback path as well as easier to be implemented than the normal PID controller, its performance could not be that satisfactory. In other cases, the designing of the PID controller should be done with the use of algorithm in order to guarantee the required control performance. 4.0. Smith Predictor control system designed using the Direct Synthesis Method iii) Design a Smith Predictor control system for the given plant with the controller designed using the Direct Synthesis Method. A block diagram must be shown to demonstrate the control system structure. The design details are also required. Smith predictor is considered to be a model-based controller whereby it is the most appropriate method for long dead time (Rao and Chidambaram 2007). The inner loop has a main controller designed without dead time. The modeling error as well as the load disturbances effects can be corrected by an outer loop. Smith predictor can as well be applied in high order systems with apparent dead time and processes that have non-minimum phase dynamics that is significant (Rao and Chidambaram 2007). The dead time occurrence in the process industry is seen to be so common. The dead time amount for most simple control loops is normally not that significant than that of the time constant. The dead time is considered to be so critical for more sophisticated control loops such as those for the quality control and it could be even longer when compared with the systems time constant (Rao and Chidambaram 2007). In case the key disturbances to the process is measured ,then the most appropriate way of coping up with the long dead time problem is through feed-forward control. There can be introduction of dead time compensation in case it is not measured accurately as well as applied in feed-forward control. Smith predictor is considered to be the most appropriate method for dead time compensation and well damped process (Rao and Chidambaram 2007). Figure 4.Smith Predictor Control system The modeling process is represented by: The load disturbance response transfer function (from d to y is: The delay-free response yp prediction is achieved with the use of internal model Gp in Smith predictor. The desired point ydp is then compared with prediction yp in order to make decision of the adjustment required(control u).There is also comparison of prediction y1(dead time is considered here) with the actual process output in order to prevent rejection as well as drifting of external disturbances. There is feedback of dy=y-y1 gap through filter F which is known to contribute to the error signal. Smith predictor scheme application needs; firstly, the process dynamics Gp model as well as process dead time estimate tau. Secondly, appropriate settings for filter dynamics and compensator Below is employed basing on the process model (dead time; 12min and delay time 10min) The first order filter is employed for F with 30 seconds as the time constant in order to capture the disturbances of low frequency. F=1/ (30*s+1) F.InputName =dy F.outputname =dp The PI controller is redesigned for C. In this case, the entire plant is under the PI controller that includes dynamics from Gp, p, dead time and F. A controller design method that is in the settings of Smith predictor is a method that is normally used for process integration with dead time. The method is mostly used in the process with high –order integration as well as in low-order without process model integration. 5.0. Simulation of the three control systems iv). Simulate the three control systems designed using the three methods with a unity step input for 100 minutes. The simulation must use one Simulink model with three sub-models, each for a control system. Display the Simulink model and sub-models, and present the simulation parameter setting. Display the three outputs and the set-point in one figure for comparison. Display also the three corresponding control variables in another figure. Compare the three output curves and comment on the performances of the three control systems. The three control systems can be designed using the below equation where Δt=0.1 sec is the sampling period The controller is Figure 5. Simulink for the three control systems The above consist of both discrete-time and continuous time simulation. In this case, the controller is discrete while the process is continuous. The sampling time is set at 0.1 sec. After the simulink model was ran, below was obtained Figure 6. Output of the three controller systems Basing on the above figure 6, it is clearly evident that the output marked in red is smoother than the rest (Fine tuned output). The one marked in green is the least. The one marked in red corresponds to a set point of 23 or gain 3.The output marked in blue corresponds to gain 2 and the output marked green corresponds to gain 1. In this case, if improvement is to be made, then a smaller sample time is required where a more accurate estimation can be employed to obtain a controller. The Kc is observed to be reduced for the case of output marked in green when compared to the other two outputs. In this case, if improvement is to be made, then a smaller sample time is required where a more accurate estimation can be employed to obtain a controller. 6.0. Discussion and conclusion Sampling operation is as well seen to have an impact on the stability translation characteristics from discrete to continuous time. Seborg and Mellichamp (2011) studied the digital controllers (1st order together with time delay processes) with the use of ultimate controller gain Kcu concept as well as ultimate period. It has been demonstrated that the results which are not uniform are as a result of sampling operation. A 1.7 gain margin is seen to be typical for a controller that is fine tuned. Δt values that are larger are seen to slow the change and response for both the ultimate period and Kc/Kcu ratio (Ogata 1997). Smith predictor is considered to be model-based controller whereby it is most appropriate for long dead time (Rao and Chidambaram 2007). The inner loop has a main controller designed without dead time. The modeling error as well as the load disturbances effects can be corrected by an outer loop. Controller tuning enables process optimization as well as error minimization between the process variables and the set point. There are different controller tuning methods that include process reaction curve and trial and error method. Cohen-Coon and Ziegler-Nichols are the most commonly used methods and they are applied in cases there are no system mathematical model. References Seborg, Edgar and Mellichamp.(2011). “Process dynamics and control, Edition:3rd, Publisher:McGraw-Hill,” ISBN: 978-0-470-64610-6 Ogata, K. (1997). “Modern Control Engineering, Edition:3rd,Prentice Hall International,” ISBN: 0-13-261389-1 Rao, V. S, and Chidambaram M. (2007)."Set point weighted modified Smith predictor for integrating and double integrating processes with time delay," ISA Transactioons, vol. 46, pp. 59-71 Read More